Ive worked pizza jobs and I can't think of why you WOULDNT slice the cheese in-house, it takes less than five minutes to do!
At least at our place it was the same machine that stirred the dough. Cut a block into 1/8 slices (a 2 min job max) and then feed each chunk into the chute and let gravity do it's thing
Fresh sliced cheese for pizzas in five minutes or less, and it adds like 2 dishes to the pile
To add further to what makes "pizza mix" or "meltable mix" better is that it uses LOW MOISTURE mozzarella cheese. Regular mozz is super wet and doesn't melt the way you expect pizza cheese to
I make my own mix at home using 1/4 lb blocks of low moisture full fat (can get at Walmart shockingly often) and 1/6 lb of a sharp cheddar